A family of area-minimizing tensor varieties

Abstract

By using Lawlor's curvature criterion, we prove that a class of real tensor varieties are regular area-minimizing cones except for one case, which gives a partial generalization of their minimality as in \cite{HKV23}. Such area-minimizing tensor varieties have not been found beyond matrix varieties. Moreover, we provide a new derivation for the important Lawlor ODE.

To appear in Proceedings of the AMS